Subgroups — C₃₁×#25651 #21482410

Order 7936.

1002 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#557	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#487	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁×#477	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2567	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#2043	C₂	1	4	yes	maximal
6	C₃₁×#1984	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#1981	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#1863	C₂	1	4	yes	maximal
9	C₄×C₃₁×#103	C₂	1	1	yes	maximal, characteristic
10	C₃₁×#557	—	2	4	no	—
11	C₃₁×#557	—	2	4	no	—
12	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
13	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×#125	—	2	2	no	—
16	C₂×C₃₁×#125	—	2	1	no	—
17	C₂×C₄×Q₈×C₃₁	—	2	1	no	—
18	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
21	C₃₁×#487	—	2	4	no	—
22	C₃₁×#477	—	2	4	no	—
23	C₂×C₃₁×#107	C₂²	1	2	yes	—
24	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#103	C₂²	1	4	yes	—
26	C₂×C₃₁×#103	C₂²	1	4	yes	—
27	C₂×C₃₁×#103	C₂²	1	2	yes	—
28	C₂×C₃₁×#103	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
30	C₃₁×#395	—	2	2	no	—
31	C₃₁×#391	—	2	1	no	—
32	C₃₁×#389	C₂²	1	4	yes	—
33	C₃₁×#384	—	2	1	no	—
34	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₃₁×#340	C₂²	1	2	yes	—
36	C₃₁×#336	C₂²	1	4	yes	—
37	C₂²×Q₈×C₃₁	—	2	1	no	—
38	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
39	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
40	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
42	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
43	C₃₁×C₄⋊Q₈	—	2	4	no	—
44	C₃₁×C₄⋊Q₈	—	2	4	no	—
45	C₃₁×C₄⋊Q₈	—	2	2	no	—
46	C₃₁×C₄⋊Q₈	—	2	2	no	—
47	C₃₁×C₄⋊Q₈	—	2	2	no	—
48	C₃₁×C₄⋊Q₈	D₄	1	4	yes	—
49	C₃₁×#125	—	2	16	no	—
50	C₃₁×#125	—	2	8	no	—
51	C₄×Q₈×C₃₁	—	2	8	no	—
52	C₄×Q₈×C₃₁	—	2	4	no	—
53	C₄×Q₈×C₃₁	—	2	4	no	—
54	C₄×Q₈×C₃₁	—	2	2	no	—
55	C₄×Q₈×C₃₁	—	2	2	no	—
56	C₄×Q₈×C₃₁	—	2	2	no	—
57	C₄×Q₈×C₃₁	D₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
66	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
71	C₂×C₄²×C₃₁	—	2	2	no	—
72	C₂×C₄²×C₃₁	—	2	1	no	—
73	C₂×C₄²×C₃₁	—	2	1	no	—
74	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
75	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
76	C₃₁×#107	—	2	4	no	—
77	C₃₁×C₄⋊C₈	—	2	2	no	—
78	C₃₁×#103	—	2	4	no	—
79	C₃₁×#103	—	2	8	no	—
80	C₃₁×#103	—	2	8	no	—
81	C₃₁×#103	—	2	4	no	—
82	C₄×C₈×C₃₁	—	2	2	no	—
83	C₃₁×#95	—	2	1	no	—
84	C₃₁×#95	—	2	4	no	—
85	C₂×Q₈×C₃₁	—	2	2	no	—
86	C₂×Q₈×C₃₁	—	2	2	no	—
87	C₂×Q₈×C₃₁	—	2	2	no	—
88	C₂×Q₈×C₃₁	—	2	1	no	—
89	C₂×Q₈×C₃₁	—	2	2	no	—
90	C₂×Q₈×C₃₁	—	2	4	no	—
91	C₂×Q₈×C₃₁	—	2	2	no	—
92	C₂×Q₈×C₃₁	—	2	4	no	—
93	C₂×Q₈×C₃₁	—	4	2	no	—
94	C₂×Q₈×C₃₁	—	8	2	no	—
95	C₂×Q₈×C₃₁	Q₁₆	1	4	yes	—
96	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	—
97	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₃₁	—	2	2	no	—
99	C₂²×C₄×C₃₁	—	2	1	no	—
100	C₂²×C₄×C₃₁	—	2	2	no	—
101	C₂²×C₄×C₃₁	—	2	1	no	—
102	C₂²×C₄×C₃₁	—	2	2	no	—
103	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
108	C₂×C₈×C₃₁	—	2	2	no	—
109	C₂×C₈×C₃₁	—	2	2	no	—
110	C₂×C₈×C₃₁	—	2	4	no	—
111	C₂×C₈×C₃₁	—	2	2	no	—
112	C₂×C₈×C₃₁	—	2	2	no	—
113	C₄⋊C₄×C₃₁	—	2	8	no	—
114	C₄⋊C₄×C₃₁	—	2	8	no	—
115	C₄⋊C₄×C₃₁	—	2	8	no	—
116	C₄⋊C₄×C₃₁	—	2	4	no	—
117	C₄⋊C₄×C₃₁	—	2	4	no	—
118	C₄⋊C₄×C₃₁	—	2	4	no	—
119	C₄⋊C₄×C₃₁	—	2	4	no	—
120	C₄⋊C₄×C₃₁	—	2	2	no	—
121	C₄⋊C₄×C₃₁	—	2	1	no	—
122	C₄⋊C₄×C₃₁	—	2	2	no	—
123	C₄⋊C₄×C₃₁	—	2	2	no	—
124	C₄⋊C₄×C₃₁	—	2	2	no	—
125	C₄⋊C₄×C₃₁	—	4	2	no	—
126	C₄⋊C₄×C₃₁	—	8	4	no	—
127	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₃₁	#41	1	4	yes	—
129	C₄²×C₃₁	—	2	8	no	—
130	C₄²×C₃₁	—	2	4	no	—
131	C₄²×C₃₁	—	2	2	no	—
132	C₄²×C₃₁	—	2	2	no	—
133	C₄²×C₃₁	—	4	2	no	—
134	C₄²×C₃₁	C₂×D₄	1	2	yes	—
135	C₄²×C₃₁	C₂×D₄	1	2	yes	—
136	#25651	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
138	Q₈×C₃₁	—	2	8	no	—
139	Q₈×C₃₁	—	2	2	no	—
140	Q₈×C₃₁	—	2	2	no	—
141	Q₈×C₃₁	—	2	8	no	—
142	Q₈×C₃₁	—	4	2	no	—
143	Q₈×C₃₁	—	4	2	no	—
144	Q₈×C₃₁	—	4	2	no	—
145	Q₈×C₃₁	—	8	4	no	—
146	C₂×C₄×C₃₁	—	2	2	no	—
147	C₂×C₄×C₃₁	—	2	2	no	—
148	C₂×C₄×C₃₁	—	2	2	no	—
149	C₂×C₄×C₃₁	—	2	2	no	—
150	C₂×C₄×C₃₁	—	2	2	no	—
151	C₂×C₄×C₃₁	—	2	4	no	—
152	C₂×C₄×C₃₁	—	2	2	no	—
153	C₂×C₄×C₃₁	—	2	4	no	—
154	C₂×C₄×C₃₁	—	2	4	no	—
155	C₂×C₄×C₃₁	—	4	2	no	—
156	C₂×C₄×C₃₁	—	4	4	no	—
157	C₂×C₄×C₃₁	—	4	2	no	—
158	C₂×C₄×C₃₁	—	4	2	no	—
159	C₂×C₄×C₃₁	—	4	2	no	—
160	C₂×C₄×C₃₁	—	4	2	no	—
161	C₂×C₄×C₃₁	—	4	4	no	—
162	C₂×C₄×C₃₁	#120	1	2	yes	—
163	C₂×C₄×C₃₁	#120	1	2	yes	—
164	C₂×C₄×C₃₁	C₂×Q₁₆	1	4	yes	—
165	C₂×C₄×C₃₁	C₂×Q₁₆	1	2	yes	—
166	C₂×C₄×C₃₁	#137	1	2	yes	—
167	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
170	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
171	C₈×C₃₁	—	4	2	no	—
172	C₈×C₃₁	—	4	2	no	—
173	C₂×#557	C₂×C₃₁	1	1	yes	characteristic
174	C₂×#487	C₂×C₃₁	1	1	yes	characteristic
175	C₂×#477	C₂×C₃₁	1	1	yes	characteristic
176	#2567	C₂×C₃₁	1	1	yes	characteristic
177	#2043	C₂×C₃₁	1	4	yes	—
178	#1984	C₂×C₃₁	1	1	yes	characteristic
179	#1981	C₂×C₃₁	1	1	yes	characteristic
180	#1863	C₂×C₃₁	1	4	yes	—
181	C₄×#103	C₂×C₃₁	1	1	yes	characteristic
182	C₂²×C₃₁	C₂×#120	1	1	yes	characteristic
183	C₂²×C₃₁	#548	1	2	yes	—
184	C₂²×C₃₁	C₂²×Q₁₆	1	1	yes	characteristic
185	C₂²×C₃₁	C₂×#137	1	1	yes	characteristic
186	C₂²×C₃₁	#577	1	2	yes	—
187	C₄×C₃₁	—	2	4	no	—
188	C₄×C₃₁	—	2	2	no	—
189	C₄×C₃₁	—	4	4	no	—
190	C₄×C₃₁	—	4	2	no	—
191	C₄×C₃₁	—	4	4	no	—
192	C₄×C₃₁	—	4	2	no	—
193	C₄×C₃₁	—	4	2	no	—
194	C₄×C₃₁	—	8	2	no	—
195	C₄×C₃₁	#451	1	4	yes	—
196	C₄×C₃₁	#532	1	1	yes	characteristic
197	C₄×C₃₁	#536	1	1	yes	characteristic
198	C₄×C₃₁	#547	1	2	yes	—
199	#557	—	2	4	no	—
200	#557	—	2	4	no	—
201	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
202	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
203	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
204	C₂×#125	—	2	1	no	—
205	C₂×#125	—	2	2	no	—
206	C₂×C₄×Q₈	—	2	1	no	—
207	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
208	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
209	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
210	#487	—	2	4	no	—
211	#477	—	2	4	no	—
212	C₂×#107	C₂²×C₃₁	1	2	yes	—
213	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
214	C₂×#103	C₂²×C₃₁	1	2	yes	—
215	C₂×#103	C₂²×C₃₁	1	4	yes	—
216	C₂×#103	C₂²×C₃₁	1	4	yes	—
217	C₂×#103	C₂²×C₃₁	1	2	yes	—
218	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
219	#395	—	2	2	no	—
220	#391	—	2	1	no	—
221	#389	C₂²×C₃₁	1	4	yes	—
222	#384	—	2	1	no	—
223	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
224	#340	C₂²×C₃₁	1	2	yes	—
225	#336	C₂²×C₃₁	1	4	yes	—
226	C₂×C₃₁	#2432	1	1	yes	characteristic
227	C₂×C₃₁	C₂×#451	1	1	yes	characteristic
228	C₂×C₃₁	#3010	1	1	yes	characteristic
229	C₂×C₃₁	#3363	1	2	yes	—
230	C₂×C₃₁	#3372	1	2	yes	—
231	C₂²×Q₈	—	2	1	no	—
232	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
233	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
234	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
236	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
237	C₄⋊Q₈	—	2	4	no	—
238	C₄⋊Q₈	—	2	4	no	—
239	C₄⋊Q₈	—	2	2	no	—
240	C₄⋊Q₈	—	2	2	no	—
241	C₄⋊Q₈	—	2	2	no	—
242	C₄⋊Q₈	D₄×C₃₁	1	4	yes	—
243	#125	—	2	16	no	—
244	#125	—	2	8	no	—
245	C₄×Q₈	—	2	8	no	—
246	C₄×Q₈	—	2	4	no	—
247	C₄×Q₈	—	2	4	no	—
248	C₄×Q₈	—	2	2	no	—
249	C₄×Q₈	—	2	2	no	—
250	C₄×Q₈	—	2	2	no	—
251	C₄×Q₈	D₄×C₃₁	1	4	yes	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	4	no	—
260	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
261	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	—	2	1	no	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
269	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
270	#107	—	2	4	no	—
271	C₄⋊C₈	—	2	2	no	—
272	#103	—	2	4	no	—
273	#103	—	2	8	no	—
274	#103	—	2	8	no	—
275	#103	—	2	4	no	—
276	C₄×C₈	—	2	2	no	—
277	#95	—	2	1	no	—
278	#95	—	2	4	no	—
279	C₃₁	#25651	1	1	yes	characteristic, direct product factor, Sylow
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	—	4	2	no	—
289	C₂×Q₈	—	8	2	no	—
290	C₂×Q₈	Q₁₆×C₃₁	1	4	yes	—
291	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	—
292	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
299	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
302	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	4	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₄⋊C₄	—	2	8	no	—
309	C₄⋊C₄	—	2	8	no	—
310	C₄⋊C₄	—	2	8	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	8	4	no	—
322	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
323	C₄⋊C₄	#41×C₃₁	1	4	yes	—
324	C₄²	—	2	8	no	—
325	C₄²	—	2	4	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	4	2	no	—
329	C₄²	C₂×D₄×C₃₁	1	2	yes	—
330	C₄²	C₂×D₄×C₃₁	1	2	yes	—
331	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
332	Q₈	—	2	8	no	—
333	Q₈	—	2	2	no	—
334	Q₈	—	2	2	no	—
335	Q₈	—	2	8	no	—
336	Q₈	—	4	2	no	—
337	Q₈	—	4	2	no	—
338	Q₈	—	4	2	no	—
339	Q₈	—	8	4	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	C₃₁×#120	1	2	yes	—
357	C₂×C₄	C₃₁×#120	1	2	yes	—
358	C₂×C₄	C₂×Q₁₆×C₃₁	1	4	yes	—
359	C₂×C₄	C₂×Q₁₆×C₃₁	1	2	yes	—
360	C₂×C₄	C₃₁×#137	1	2	yes	—
361	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
362	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
363	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
364	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
365	C₈	—	4	2	no	—
366	C₈	—	4	2	no	—
367	C₂²	C₂×C₃₁×#120	1	1	yes	characteristic
368	C₂²	C₃₁×#548	1	2	yes	—
369	C₂²	C₂²×Q₁₆×C₃₁	1	1	yes	characteristic
370	C₂²	C₂×C₃₁×#137	1	1	yes	characteristic
371	C₂²	C₃₁×#577	1	2	yes	—
372	C₄	—	2	4	no	—
373	C₄	—	2	2	no	—
374	C₄	—	4	4	no	—
375	C₄	—	4	2	no	—
376	C₄	—	4	4	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	2	no	—
379	C₄	—	8	2	no	—
380	C₄	C₃₁×#451	1	4	yes	—
381	C₄	C₃₁×#532	1	1	yes	characteristic
382	C₄	C₃₁×#536	1	1	yes	characteristic
383	C₄	C₃₁×#547	1	2	yes	—
384	C₂	C₃₁×#2432	1	1	yes	characteristic
385	C₂	C₂×C₃₁×#451	1	1	yes	characteristic
386	C₂	C₃₁×#3010	1	1	yes	characteristic
387	C₂	C₃₁×#3363	1	2	yes	—
388	C₂	C₃₁×#3372	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₄×Q₈×C₃₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
136. #25651	C₃₁	direct (N × H)
279. C₃₁	#25651	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃₁×#557	2
C₂×C₃₁×#487	2
C₂×C₃₁×#477	2
C₃₁×#2567	2
C₃₁×#2043	2
C₃₁×#1984	2
C₃₁×#1981	2
C₃₁×#1863	2
C₄×C₃₁×#103	2
#25651	31

Subgroups — C31×#25651 #21482410

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#25651 #21482410